Moving Extreme Ranked Set Sampling Research Articles

Large sample properties of maximum likelihood estimator using moving extremes ranked set sampling

Large sample properties of maximum likelihood estimator using moving extremes ranked set sampling

Estimation of Population Size Using Ranked Set Sampling and Some of its Variations

The purpose of this paper is to estimate the population size of known total, using a sample that chosen using ranked set sampling technique and some of its variations; in particular, Ranked Set Sampling (RSS), Moving Extreme Ranked Set Sampling (MERSS) and Median Ranked Set(MRSS) are considered. The estimators obtained are compared with their counterparts using simple random sampling(SRS). It turned out that the estimators using RSS and its variations are more efficient than the corresponding estimators using SRS.

New modification of ranked set sampling for estimating population mean

A key problem in statistics and machine learning is drawing samples from a population. The drawn sample is mainly used to make inferences about the factors and characteristics of the population in order to make high-accuracy estimations. This study developed a new sampling method called Except Extreme Ranked Set Sampling (EERSS) for estimating the population mean. EERSS estimator is compared with its counterparts by using Simple Random Sampling (SRS), Ranked Set Sampling (RSS), Median Ranked Set Sampling (MRSS), and Moving Extreme Ranked Set Sampling (MERSS). Simulation study and real data sets are used for illustrations and comparisons. It shows that the EERSS estimator is an unbiased estimator of the population mean for symmetric distributions and it is the most efficient among all estimators.

Sampling Information for Generalized Rayleigh Distribution with Application to Parameter Estimation

In the current paper, we considered the Fisher information matrix from generalized Rayleigh distribution (GR) distribution in moving extremes ranked set sampling (MERSS). The numerical results show that the ranked set sample carry more information about $$\lambda$$ and $$\alpha$$ than a simple random sample of equivalent size. In order to give more insight into the performance of MERSS with respect to (w.r.t.) simple random sampling (SRS), a modified unbiased estimator and a modified best linear unbiased estimator (BLUE) of scale and shape $$\lambda$$ and $$\alpha$$ from GR distribution in SRS and MERSS are studied. The numerical results show that the modified unbiased estimator and the modified BLUE of $$\lambda$$ and $$\alpha$$ in MERSS are significantly more efficient than the ones in SRS.

Estimation of System Reliability Based on Moving Extreme and MiniMax Ranked Set Sampling for Exponential Distributions

Estimation of System Reliability Based on Moving Extreme and MiniMax Ranked Set Sampling for Exponential Distributions

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the Fisher information matrix for the location-scale family. The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS. In order to give more insight into the performance of MERSS with respect to simple random sampling, the Fisher information matrix for usual location-scale distributions are respectively computed under the two sampling. The numerical results show that MERSS provides more information than simple random sampling in parametric inference.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Estimation of the distribution function using moving extreme and MiniMax ranked set sampling

Recently, MiniMax ranked set sampling (MiniMax RSS) scheme is suggested for population mean estimation. In this article, we consider moving extreme ranked set sampling (MERSS) and MiniMax RSS for estimating the distribution function of a random variable. Using the maximum likelihood estimation method, new estimators of the cumulative distribution function (CDF) are derived and also their variances are obtained. In the light of a simulation study, we conclude that the estimators based on MiniMax RSS work well compared to those based on MERSS setups regardless of the ranking quality. Additionally, the proposed concomitant-based CDF estimators tend to be superior to their analogs as long as the ranking process is done with fairly good accuracy. For the sake of illustration, two empirical datasets are considered to show the applicability of the proposed estimators in practice.

Log-extended exponential-geometric parameters estimation using simple random sampling and moving extremes ranked set sampling

In this paper, estimation of parameters α and β for the log-extended exponential-geometric distribution will be respectively considered in cases when β is known and when both are unknown. Simple random sampling (SRS) and moving extremes ranked set sampling (MERSS) will be used, and several traditional estimators will be considered. The estimators using MERSS are compared to the corresponding ones using SRS. The numerical results show that the estimators using MERSS are significantly more efficient than the ones using SRS. A real data set is used for illustration.

Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability

In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures.

Pareto parameters estimation using moving extremes ranked set sampling

Cost effective sampling is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the scale and shape parameters $$\theta $$ and $$\alpha $$ from $$p(\theta , \alpha )$$ . Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS. A real data set is used for illustration.

Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method

In general, survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Models for survival data have frequently been based on the proportional hazards model, proposed by Cox. The Cox model has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This paper demonstrates that this approach provides a more powerful testing procedure as well as a more efficient estimate of hazard ratio than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural study data are used to illustrate the methods developed in this paper.

Reducing sample size needed for accelerated failure time model using more efficient sampling methods

Survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Accelerated failure time (AFT) models provide a linear relationship between the log of the failure time and covariates that affect the expected time to failure by contracting or expanding the time scale. The AFT model has intensive application in the field of social, medical, behavioral, and public health sciences. In this article we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) or an Extreme Ranked Set Sampling (ERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This article demonstrates that these approaches provide a more powerful testing procedure, as well as a more efficient estimate of hazard ratio, than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural Health Study data are used to illustrate the methods developed in this article.

Modified Maximum Likelihood Estimator of Scale Parameter Using Moving Extremes Ranked Set Sampling

A modified maximum likelihood estimator (MMLE) of scale parameter is considered under moving extremes ranked set sampling (MERSS), and its properties are obtained. For some usual scale distributions, we obtain explicit form of the MMLE and prove the MMLE is an unbiased estimator under MERSS. The simulation results show that the MMLE using MERSS is always more efficient than the MLE using simple random sampling, when the same sample size is used. The simulation results also show that the loss of efficiency in using the MMLE instead of the MLE is very small for small sample.

More efficient logistic analysis using moving extreme ranked set sampling

ABSTRACTLogistic regression is the most popular technique available for modeling dichotomous-dependent variables. It has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient logistic regression analysis based on moving extreme ranked set sampling (MERSSmin) scheme with ranking based on an easy-to-available auxiliary variable known to be associated with the variable of interest (response variable). The paper demonstrates that this approach will provide more powerful testing procedure as well as more efficient odds ratio and parameter estimation than using simple random sample (SRS). Theoretical derivation and simulation studies will be provided. Real data from 2011 Youth Risk Behavior Surveillance System (YRBSS) data are used to illustrate the procedures developed in this paper.

Inference on Downton’s Bivariate Exponential Distribution Based on Moving Extreme Ranked Set Sampling

The purpose of this paper is to estimate the parameters of Downton’sbivariate exponential distribution using moving extreme ranked set sampling(MERSS). The estimators obtained are compared via their biases andmean square errors to their counterparts using simple random sampling (SRS).Monte Carlo simulations are used whenever analytical comparisons are difficult.It is shown that these estimators based on MERSS with a concomitantvariable are more efficient than the corresponding ones using SRS. Also,MERSS with a concomitant variable is easier to use in practice than RSS witha concomitant variable. Furthermore, the best unbiased estimators among allunbiased linear combinations of the MERSS elements are derived for someparameters.

Of Ranking in Moving Extreme Ranked Set Sampling

of Ranking in Moving Extreme Ranked Set Sampling

Bayesian Estimation of the Mean of Exponential Distribution Using Moving Extremes Ranked Set Sampling

In this paper, Bayesian estimation for the mean of exponential distribution is considered using moving extremes ranked set sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and simple random sampling (SRS) methods. Properties of the suggested estimators are investigated under SRS and MERSS. It is found that the suggested estimators using MERSS are more efficient than their counterparts based on SRS for all cases considered in this study.